Question

Find the minimum value of 3 cos x+4 sin X+5

Answer 1

Answer:

10

Step-by-step explanation:

Thanks for the query!!

Prerequisites:

Maximum Value of a equation involving Sin and Cos can be found by using formula : √ ( a² + b² ). Here, a refers to coefficient of Sin function and b refers to coefficient of Cos function.

Query: Maximum value of 3 Cos x + 4 Sin x + 5

According to the question,

⇒ a = 4 and b = 3

Hence applying in the formula we get,

⇒ √ ( 3² + 4² ) = √ 25 = ± 5

Now we know that greatest value can be obtained only if we use positive value. Hence Substituting the maximum value of 3 Cos x + 4 Sin x we get,

⇒ 5 + 5 = 10

Hence the maximum possible value for 3 Cos x + 4 Sin x + 5 is 10.